|
on Economic Design |
| By: | Jason Hartline; Aleck Johnsen; Yingkai Li |
| Abstract: | We study auctions that are robust at any scale, i.e., they can be applied to sell both expensive and cheap items and achieve the best multiplicative approximations of the optimal revenue in the worst case. We show that the optimal mechanism is scale invariant, which randomizes between selling at the second-price and a 2.45 multiple of the second-price. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.21231 |
| By: | Dube, Devwrat |
| Abstract: | This paper introduces a combinatorial optimisation problem that we call the knapsack sequencing problem (KSP). KSP arises when the server in a sequencing problem is constrained to work in fixed-duration shifts. Each shift can be viewed as a knapsack, but unlike standard knapsack or bin-packing problems, KSP incorporates a temporal structure that distinguishes early and late shifts. The main challenge lies not in incentivising truth-telling but in algorithmically identifying the optimal partition of agents into shifts; a challenge compounded by the fact that KSP is strongly NP-hard, with the decision version being strongly NP-complete. We propose necessary conditions that efficient sequencing rules must satisfy, which help reduce the search space for feasible partitions. We show that the Vickrey–Clarke–Groves (VCG) mechanism, using the efficient sequencing rule and VCG transfers, is strategy-proof for KSP. We establish the existence of first-best mechanisms—mechanisms that are efficient, strategy-proof, and budget balanced—for a subclass (unit-capacity) of KSP requiring n shifts to serve n agents. We also show, via a three-agent example, that when budget balance is imposed together with efficiency, strategy-proofness may fail. This research highlights the difficulties in extending classical sequencing results to settings with shift constraints and contributes both theoretical insights and algorithmic considerations relevant to resource allocation mechanisms. |
| Keywords: | Knapsack Sequencing Problem, Combinatorial Optimisation, Mechanism Design, VCG Mechanisms, Strategy-proofness, Budget-balance, Computational Complexity |
| JEL: | C61 C63 D61 D82 |
| Date: | 2025–10–25 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126600 |
| By: | Andrea Attar (CEIS & DEF University of Rome "Tor Vergata"); Eloisa Campioni (CEIS & DEF University of Rome "Tor Vergata"); Thomas Mariotti (Toulouse School of Economics, CNRS); Alessandro Pavan (Northwestern University) |
| Abstract: | We study the design of market information in competing-mechanism games. We identify a new dimension, private disclosures, whereby the principals asymmetrically inform the agents of how their mechanisms operate. We show that private disclosures have two important effects. First, they can raise a principal's payoff guarantee against her competitors' threats. Second, they can support equilibrium outcomes and payoffs that cannot be supported with standard mechanisms. These results call for a novel approach to competing mechanisms, which we develop to identify a canonical game and a canonical class of equilibria, thereby establishing a new revelation principle for this class of environments. |
| Keywords: | Incomplete Information, Competing Mechanisms, Private Disclosures, Revelation Principle. |
| JEL: | D82 |
| Date: | 2025–06–28 |
| URL: | https://d.repec.org/n?u=RePEc:rtv:ceisrp:615 |
| By: | Sarah Kühn (first name last name) (Paderborn University) |
| Abstract: | Child care allocation markets in Germany widely employ variants of the Gale-Shapley Deferred Acceptance (DA) mechanism (Gale & Shapley, 1962) to match children to child care centers. However, implementers often make seemingly minor adjustments to the original mechanism without thoroughly evaluating their implications. We show that these adjustments can significantly affect a mechanism’s desirable properties. Adjustments are necessary on these markets as care durations, capturing the contractual terms agreed upon by children and child care centers, are key to finding an allocation. Thus, we model a child care allocation problem with care durations. We demonstrate how the cumulative offer process, as developed for matching with contracts (Hatfield & Milgrom, 2005), can be effectively adapted to our context. However, a key practical disadvantage is that this mechanism requires full preference disclosure from participants, which is often unrealizable in real-world settings. We analyze how existing practical implementations of the DA deal with incomplete preference elicitation and examine the implications of these approaches. Our comparative analysis reveals that one mechanism from practice offers a distinct advantage over the others when considering incomplete preference elicitation. (abstract of the paper) |
| Keywords: | Deferred Acceptance, Stability, Strategy-Proofness, Preference elicitation, Matching with contracts (keywords) |
| JEL: | C78 D47 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:162 |
| By: | Flora C. Shi; Martin J. Wainwright; Stephen Bates |
| Abstract: | We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.21178 |
| By: | Alejandro Francetich; Burkhard C. Schipper |
| Abstract: | We consider a principal who wishes to screen an agent with \emph{discrete} types by offering a menu of \emph{discrete} quantities and \emph{discrete} transfers. We assume that the principal's valuation is discrete strictly concave and use a discrete first-order approach. We model the agent's cost types as non-integer, with integer types as a limit case. Our modeling of cost types allows us to replicate the typical constraint-simplification results and thus to emulate the well-treaded steps of screening under a continuum of contracts. We show that the solutions to the discrete F.O.C.s need not be unique \textit{even under discrete strict concavity}, but we also show that there cannot be more than two optimal contract quantities for each type, and that -- if there are two -- they must be adjacent. Moreover, we can only ensure weak monotonicity of the quantities \textit{even if virtual costs are strictly monotone}, unless we limit the ``degree of concavity'' of the principal's utility. Our discrete screening approach facilitates the use of rationalizability to solve the screening problem. We introduce a rationalizability notion featuring robustness with respect to an open set of beliefs over types called \textit{$\Delta$-O Rationalizability}, and show that the set of $\Delta$-O rationalizable menus coincides with the set of usual optimal contracts -- possibly augmented to include irrelevant contracts. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.20921 |
| By: | Alejandro Francetich; Burkhard C. Schipper |
| Abstract: | We analyze a principal-agent procurement problem in which the principal (she) is unaware some of the marginal cost types of the agent (he). Communication arises naturally as some types of the agent may have an incentive to raise the principal's awareness (totally or partially) before a contract menu is offered. The resulting menu must not only reflect the principal's change in awareness, but also her learning about types from the agent's decision to raise her awareness in the first place. We capture this reasoning in a discrete concave model via a rationalizability procedure in which marginal beliefs over types are restricted to log-concavity, ``reverse'' Bayesianism, and mild assumptions of caution. We show that if the principal is ex ante only unaware of high-cost types, all of these types have an incentive raise her awareness of them -- otherwise, they would not be served. With three types, the two lower-cost types that the principal is initially aware of also want to raise her awareness of the high-cost type: Their quantities suffer no additional distortions and they both earn an extra information rent. Intuitively, the presence of an even higher cost type makes the original two look better. With more than three types, we show that this intuition may break down for types of whom the principal is initially aware of so that raising the principal's awareness could cease to be profitable for those types. When the principal is ex ante only unaware of more efficient (low-cost) types, then \textit{no type} raises her awareness, leaving her none the wiser. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.20918 |
| By: | Javier Cembrano; Felix Fischer; Max Klimm |
| Abstract: | We study the selection of agents based on mutual nominations, a theoretical problem with many applications from committee selection to AI alignment. As agents both select and are selected, they may be incentivized to misrepresent their true opinion about the eligibility of others to influence their own chances of selection. Impartial mechanisms circumvent this issue by guaranteeing that the selection of an agent is independent of the nominations cast by that agent. Previous research has established strong bounds on the performance of impartial mechanisms, measured by their ability to approximate the number of nominations for the most highly nominated agents. We study to what extent the performance of impartial mechanisms can be improved if they are given a prediction of a set of agents receiving a maximum number of nominations. Specifically, we provide bounds on the consistency and robustness of such mechanisms, where consistency measures the performance of the mechanisms when the prediction is accurate and robustness its performance when the prediction is inaccurate. For the general setting where up to $k$ agents are to be selected and agents nominate any number of other agents, we give a mechanism with consistency $1-O\big(\frac{1}{k}\big)$ and robustness $1-\frac{1}{e}-O\big(\frac{1}{k}\big)$. For the special case of selecting a single agent based on a single nomination per agent, we prove that $1$-consistency can be achieved while guaranteeing $\frac{1}{2}$-robustness. A close comparison with previous results shows that (asymptotically) optimal consistency can be achieved with little to no sacrifice in terms of robustness. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.19002 |
| By: | Cetin, Umut; Danilova, Albina |
| Abstract: | Does retail order internalization benefit (via price improvement) or harm (via reduced liquidity) retail traders? To answer this question, we compare two market designs that differ in their mode of liquidity provision: In the setting capturing retail order internalization, liquidity is provided by market makers (wholesalers) competing for the retail order flow in a Bertrand fashion. Instead, in the open exchange setting, price-taking competitive agents act as liquidity providers. We discover that, when liquidity providers are risk averse, routing of marketable orders to wholesalers is preferred by all retail traders: informed, uninformed, and noise. Furthermore, most measures of liquidity are unaffected by the market design. We also identify a universal parameter that allows comparison of market liquidity, profit and value of information across different markets. |
| JEL: | C1 |
| Date: | 2025–10–20 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:129686 |
| By: | Debasis Mishra; Soumendu Sarkar; Arunava Sen; Jay Sethuraman; Sonal Yadav |
| Abstract: | The Right to Free and Compulsory Education Act (2009) (RTE) of the Government of India prescribes student-teacher ratios for state-run schools. One method advocated by the Act to achieve its goals is the redeployment of teachers from surplus to deficit (in teacher strength) schools. We consider a model where teachers can either remain in their initially assigned schools or be transferred to a deficit school in their acceptable set. The planner's objective is specified in terms of the post-transfer deficit vector that can be achieved. We show that there exists a transfer whose post-transfer deficit vector Lorenz dominates all achievable post-transfer deficit vectors. We provide a two-stage algorithm to derive the Lorenz-dominant post-transfer deficit vector, and show that this algorithm is strategy-proof for teachers. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.18708 |
| By: | David Lagziel; Ehud Lehrer |
| Abstract: | We examine information structures in settings with privately informed agents and an informationally constrained mediator who supplies additional public signals. Our focus is on characterizing the set of posteriors that the mediator can induce. To this end, we employ a graph-theoretic framework: states are represented as vertices, information sets correspond to edges, and a likelihood ratio function on edges encodes the posterior beliefs. Within this framework, we derive necessary and sufficient conditions, internal and external consistency, for the rationalization of posteriors. Finally, we identify conditions under which a single mediator can implement multiple posteriors, effectively serving as a generator of Blackwell experiments. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.20986 |
| By: | Roberto Corrao; Joel P. Flynn; Karthik Sastry |
| Abstract: | We introduce a model of incentive contracting in which the principal, in addition to writing contracts, must engage in contractibility design: creating an evidence structure that allows them to prove when the agent has breached the contract. Designing an evidence structure entails both (i) front-end costs borne ex ante, such as those of drafting contracts, and (ii) back-end costs borne ex post, such as those of generating evidence. We find that, under even small front-end costs, optimal contracts are coarse, specifying finitely many contingencies out of a continuum of possibilities. In contrast, under even large back-end costs, optimal contracts are complete. Applied to the design of procurement contracts, our results rationalize: (i) the discreteness of contracts, (ii) the presence of similarly vague contracts in low-stakes and high-stakes settings, and (iii) the discontinuous adjustment of contracts to changes in the economic environment. |
| JEL: | D82 D86 K0 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34379 |
| By: | Hideo Konishi (Department of Economics, Boston College); Michel Le Breton (Toulouse School of Economics, Toulouse Capitole University); Shlomo Weber (Southern Methodist University) |
| Abstract: | In this paper, we define additive dyadic social interactions games (ADG), in which each player cares not only about the selected action, but also about interactions with other players, especially those who choose the same action. This class of games includes alliance formation games, network games, and discrete choice problems with network externalities. While it is known that games in the ADG class admit a pure strategy Nash equilibrium that is a maximizer of the game's potential, the potential approach does not always apply if all coalitional deviations are allowed. We then introduce a novel notion of a strong landscape equilibrium, which relies on a limited scope of coalitional deviations. We show the existence of a strong landscape equilibrium for a class of basic additive dyadic social interactions games (BADG), even though a strong Nash equilibrium may fail to exist. Somewhat surprisingly, a potential-maximizing strong landscape equilibrium is not always a strong Nash equilibrium even if the set of the latter is nonempty. We also provide applications and extensions of our results. |
| Keywords: | Social Interactions Game, Potential Function, Coalition Formation, Strong Nash Equilibrium, Strong Landscape Equilibrium |
| JEL: | C71 C72 C78 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:kyo:wpaper:1120 |
| By: | Sarah Kühn (first name last name) (Paderborn University); Nadja Papatya Duman (first name last name of second author) (Bielefeld University (workplace of second author)); Britta Hoyer (first name last name of second author) (Eberhard Karls Universität Tübingen (workplace of second author)); Thomas Streck (first name last name of second author) (Paderborn University (workplace of second author)); Nadja Stroh-Maraun (first name last name of second author) (Paderborn University (workplace of second author)) |
| Abstract: | Preferences are central to matching markets, yet experiments typically rely on induced preferences that may not reflect real-world decision-making. We examine how induced versus non-induced preferences shape behavior in matching experiments, extending Chen and Sönmez (2006). Using the most frequently used school choice mechanisms (Boston, Deferred Acceptance, and Top Trading Cycles), we supplement monetary incentives with participants’ own preferences. Our results show that preference induction systematically affects truthful reporting and comprehension of mechanisms. These findings underscore that experimental design choices matter for the validity of behavioral insights and have direct implications for policy evaluation. (abstract of the paper) |
| Keywords: | Non-induced Preferences, Experiments, Matching, School Choice (keywords) |
| JEL: | C78 D47 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:159 |
| By: | Sarah Kühn (first name last name) (Paderborn University); Nadja Stroh-Maraun (first name last name of second author) (Paderborn University (workplace of second author)) |
| Abstract: | We define neighborhood help problems where agents may seek and/or provide various kinds of help as matching markets with an explicitly modeled outside option. In most matching markets a short supply of compatible helpers may result in many agents being unmatched, forcing them to rely on costly outside options. These unmatched agents leave the market without helping and substantial potential is lost. To overcome this issue we introduce the pool option which incentivizes agents to provide help while receiving help outside the market. By explicitly modeling the outside option our model becomes applicable to a broad range of applications. The top trading cycles (TTC) mechanism (Shapley & Scarf, 1974) no longer provides a Pareto efficient allocation in this setting. Thus, we propose the neighborhood top trading cycles and chains (NTTCC) mechanism which incorporates the pool option and is based on the TTCC by Roth et al. (2004). The NTTCC is individual rational, Pareto efficient, and strategy-proof. The NTTCC (weakly) reduces overall costs compared to the TTC. More generally, the NTTCC is cost-minimal in the class of individual rational and Pareto-efficient mechanisms. (abstract of the paper) |
| Keywords: | Matching, School Choice, Kidney Exchange, Top Trading Cycles, Pareto Efficiency, Strategy-Proofness (keywords) |
| JEL: | C78 D47 |
| URL: | https://d.repec.org/n?u=RePEc:pdn:dispap:158 |